Allais Paradox and Rational Decisions

Slate has a simple test of rationality, which is really the Allais Paradox. To understand the significance of the Allais Paradox, one has to go back to the Expected Utility Theory proposed by John von Neumann and Oskar Morgenstern in 1944. According to this theory, the expected utility of a gamble or a lottery with multiple outcomes and corresponding probabilities, is simply the expectation over the utility associated with each outcome. In deciding between gambles or lotteries, the one that maximizes the expected utility is chosen. In constructing utility functions associated with the gambles or lotteries, a certain set of assumptions are made. One of the assumptions is the substitution axiom. It states that if a decision maker prefers a lottery with outcome ‘x’ over ‘y’, and if he has to then choose between two lotteries that offer x and y respectively with the same probabilities (p) and are identical otherwise, then he will still choose the one that offers ‘x’ with probability ‘p’ over the one that offers ‘y’ with the same probability ‘p’. A clearer description of this utility theory can be found here.The Allais paradox violates the substitution axiom, as demonstrated in the simple test on Slate mentioned at the beginning of this post.

It was in explaining the Allais paradox that Kahnemann and Tversky came up with their oft-cited Prospect Theory (1979). One of the observations under the Prospect Theory is that people tend to be risk-averse in prospects concerning gains, and risk-loving in prospects concerning losses. The Allais paradox and subsequent research on the role of emotions financial decision-making establishes that we are not rational when it comes to making financial decisions, much though we’d like to believe we are.